Talks are due to take place on Friday over the “accelerated accession” of Turkey as part of a deal aimed at stemming the tide of refugees heading to European Union countries.

It comes as the Home Office admitted it had not carried out a full impact assessment of what Turkish membership would mean to the UK, including the population change, despite admitting in 2011 that it was “crucial” to do so.

But according to a Survation poll of more than 2,000 people, more than one in three surveyed said they would be more likely to vote to leave the EU if Turkey became a member.

Even among those who said they intended to vote for Britain to remain part of the EU, more than a quarter (25.6 per cent) said Turkey’s accession would make them more likely to vote to leave.

Given how tight the polls are, this would be enough to swing the vote for the leave campaign.